Hi, Slav. Welcome to the neighborhood and the LTH tribe.
I'll give you a quick off-the-top-of-my-head list & I'm sure others will chime in with favorites . . . and then you can search the list for specific write-ups*.
Your easiest food concentration is on Northwest Highway around Oliphant. I can recommend Zia's [Italian], Elliot's isn't a bad steak house, and I like the specials on the menu at Don Juan's [I think they do a mediocre job with the standard Mexican-American dishes, but ymmv]. Cafe Touche isn't bad, but I find them to be a kinda overpriced for the bistro stuff they do. Tony's isn't my favorite Italian deli, but it's OK. NEVER buy a pre-made sandwich there; have them make it fresh. Conca D'Oro is a good bakery & they sell canoli shells that you can make filling for yourself . . . my mom makes me bring them to her house at Christmas.
My favorite local pizza delivery is Joe's on Higgins. I like 'em ordered with light cheese & extra crispy crust.
Chinese food in the neighborhood is hopeless. Fried Rice Express on Higgins can be edible. Sometimes.
Avoid Taco Burrito King @ Harlem and Higgins. Food for inebriates on the way home from the bar. If you want a decent taqueria, try Estella [I think it's called] at Milwaukee & Lawrence.
Basilico on Cumberland a block south of Lawrence is decent Italian-American food**.
Rich's on Harlem at Lawrence is a Polish-oriented grocery/liquor store. They have a large selection of prepared food packaged up & refrigerated to go. A default for me when I want to eat at home & the current left-overs aren't interesting to me. Produce World at Lawrence & Cumberland is an OK store; oriented toward Greek/Italian/Polish and recently some Indian food-stuffs. It just got a badly-needed face lift. MUCH better produce and ethnic food selection than any local Jewel or Dominick's, but that's damning with faint praise. I frequently go to Fresh Farms on Touhy in Niles for my produce shopping. [I've given up on the Jewel and Dominick's in the neighborhood. The one around the corner from my house at Harlem & Foster has a particularly awful produce section.]
Joseph's Market on Irving Park east of Cumberland is a very good Italian deli. They make sausage there & have a good butcher counter.
Bobo's Hot Dogs on Irving Park is across the street from Joseph's is probably the best, closest hot dog stand. [Avoid Brandy's on Harlem by the RR tracks. Bad AND over-priced.]
Jay's on Narragansett near Montrose does an Italian beef I like a lot. Get lots of giardinara.
There's another nice restaurant cluster in Edgebrook. GNR winning Elephant Thai is there. The Chocolate Shoppe sells ice cream across the street [the decorations are a must-see]. Moher is an OK Irish-type bar. Al Primo Canto does a nice Brazilian-style meat fest, but the quality was off last time I visited.
Well, that'll get you started, anyway. There's lots of interesting food in reasonable traveling distance . . . feel free to inquire about specifics.
Giovanna
*if you don't know this search trick, you can search for a specific place using google:
restaurantname site:lthforum.com
** being of Sicilian-American background, I'm very, very picky about the quality of my Italian food. Zia's and Basilico are the ONLY places in the neighborhood I'll recommend . . . and there are a lot of them.
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"Enjoy every sandwich."
-Warren Zevon